1.1k citations · 2k across the 15 of their papers we have counts for
16 papers
Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
Tatiana Kossaczká, Ameya D. Jagtap, Matthias Ehrhardt
In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The…
Learning stiff chemical kinetics using extended deep neural operators
Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee +2
We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with…
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
Michael Penwarden, Ameya D. Jagtap, Shandian Zhe +2
Physics-informed neural networks (PINNs) as a means of solving partial differential equations (PDE) have garnered much attention in the Computational Science and Engineering (CS&E)…
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis +1
In this paper, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further impr…
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
Ameya D. Jagtap, George Em Karniadakis
Inspired by biological neurons, the activation functions play an essential part in the learning process of any artificial neural network commonly used in many real-world problems.…
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
Tim De Ryck, Ameya D. Jagtap, Siddhartha Mishra
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that…
Physics-informed neural networks for inverse problems in supersonic flows
Ameya D. Jagtap, Zhiping Mao, Nikolaus Adams +1
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we…
Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations
Ameya D. Jagtap, Dimitrios Mitsotakis, George Em Karniadakis
We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre-Green-Naghdi system; it describes future state…
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis +1
Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power…
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi +1
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kr…
Parallel Physics-Informed Neural Networks via Domain Decomposition
Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis
We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs),…
A physics-informed neural network for quantifying the microstructure properties of polycrystalline Nickel using ultrasound data
Khemraj Shukla, Ameya D. Jagtap, James L. Blackshire +2
We employ physics-informed neural networks (PINNs) to quantify the microstructure of a polycrystalline Nickel by computing the spatial variation of compliance coefficients (compres…
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
Ameya D. Jagtap, Kenji Kawaguchi, George Em Karniadakis
We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep a…
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D. Jagtap, George Em Karniadakis
We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions o…
Method of Relaxed Streamline Upwinding for Hyperbolic Conservation Laws
Ameya D. Jagtap
In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on rel…
Explicit and Implicit Kinetic Streamlined-Upwind Petrov Galerkin Method for Hyperbolic Partial Differential Equations
Ameya Dilip Jagtap, S. V. Raghurama Rao
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equati…